I 100% agree with this, the hotel is a bit dated, but the service is amazing and the location just a 1 min walk from the tourist section of Hollywood Blvd is wonderfully central for doing LA. This is my go to hotel in LA.
If you are doing Disney, I recommend staying out near it. The last trip we stayed at the Super 8 near main gate (pretty sure that is what they referred to it as). Comfortable, not expensive (don't bother with the breakfast it really isn't worth the fight for a table) and only a few minutes walk to the parks & the Disney shopping area (plus a Denny's nearby if you are after, cheap, quick, 24hr food)
They can also organise a shuttle drop off & pick up for universal. (we used the service to change to a hotel near universal)
I have done both coasts, and love the Orlando area parks, but if you are watching the $$ stick with the west coast, you will get more time for your dollars since you wont have to fly across the country & as other posters have said there are a lot of other attractions not too far away from LA.
As for hiring a car in LA, can't say, never done it, but I was not convinced I would be fine driving in the LA traffic. I have driven from Vegas to Orlando and in many countries around the world, but still not confident on driving in LA.
If you (or your kids) are really into movies/tv, do the WB studio tour.
Whatever you decide, plan ahead, and read up on tips and tricks for Fastpass, etc. (those alone could be a post that goes on for months).
But mostly, have fun